Abstract / Synopsis
Textbooks may say that the so-called conic sections can be obtained from cones, but this is rarely proved. However, diagrams of the proof require no intuition for solids and can be read as flat. We construct the diagrams with ruler and compass and derive from them basic properties of conic sections as established by Apollonius of Perga, though again in a way that does not require a third dimension. The construction inevitably involves choices that give play to one’s aesthetic sense.
David Pierce, "Conic Diagrams," Journal of Humanistic Mathematics, Volume 12 Issue 2 (July 2022), pages 378-398. DOI: 10.5642/jhummath.NFHQ4170. Available at: https://scholarship.claremont.edu/jhm/vol12/iss2/19
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